McLemore and Travis Releford scored 11 each for the Jayhawks, who wearily advanced to play No. 8 seed North Carolina and former coach Roy Williams in the South Regional on Sunday.
Kansas led only briefly to start the game, and never held a lead until 1:37 left in the game, when Travis Releford's two free throws put the Jayhawks up for good.
The Jayhawks seized the lead again early in the second half when Kevin Young followed up his own miss by grabbing the rebound and throwing down a reverse jam, and then Releford scored off a nifty feed from McLemore, forcing Harper to burn a timeout.